## The Elements of Euclid |

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Page 16

22 th Book I. Because the point B is the centre of the circle CGH , BC is

22 th Book I. Because the point B is the centre of the circle CGH , BC is

**equal**e to BG ; and because D is the centre of the circle GKL , e 15. Def . DL is**equal**to DG , and DA , DB , parts of them , are**equal**; f 3. Page 17

AB to DE , and AC to DF ; A D Book I. and the angle BAC

AB to DE , and AC to DF ; A D Book I. and the angle BAC

**equal**to the angle ÉDF , the base BC shall be**equal**to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles , to which the**equal**sides are opposite , shall ... Page 18

b Book I.

b Book I.

**equal**to AC , and let the straight lines AB , AC be produced to SD and E , the angle ABC shall be**equal**to the angle ACB , and the angle CBD to the angle BCE . In BD take any point F , and from AE the greater , cut off a 3. Page 19

Let ABC be a triangle having the angle ABC

Let ABC be a triangle having the angle ABC

**equal**to the Book L angle ACB ; the side AB is also**equal**to the side Ac . For if AB be not**equal**to AC , one of them is greater than the other : let AB be the greater , and from it cut off DB ... Page 20

E fore , because AC is

E fore , because AC is

**equal**to AD in the triangle ACD , the angles ECD , FDC F upon the other side of the base CD are C a 5. 1 .**equal**to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle FDC is ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone cylinder definition demonstrated described diameter divided double draw drawn equal equal angles equiangular equimultiples excess fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise magnitude manner meet multiple Note opposite parallel parallelogram pass perpendicular plane prisms produced PROP proportionals proposition pyramid radius reason rectangle rectangle contained remaining right angles segment shown sides similar sine solid solid angle sphere square square of AC taken THEOR third triangle ABC wherefore whole